大型稀疏非线性方程组的不精确牛顿法  

Inexact Newton method for solving large and sparse systems of nonlinear equations

作　　者：杨凤红[1] 唐云[1] 何淼[1] 

机构地区：[1]清华大学数学科学系,北京100084

出　　处：《延边大学学报（自然科学版）》2003年第3期157-160,共4页Journal of Yanbian University（Natural Science Edition）

基　　金：国家重点基础研究资助项目(G1998020309)

摘　　要：将经典牛顿法与CAV(component averaging)算法结合,得到了一种易于并行的不精确牛顿法.用Broyden三对角问题和IEEE118节点的电力系统对算法进行了串行实现,并与牛顿-高斯-赛德尔法及文献[7]中的重叠分块牛顿法进行了比较.This paper proposes a new and fast inexact Newton method, called Newton-CAV method, which combines Newton method with the CAV (component averaging) algorithm suitable for solving large and sparse unstructured linear equations. The serial implementation of this method is performed on the IEEE 118-bus system and Broyden tridiagonal problem under Matlab 6.1 environment. And the numerical results are compared with both the Newton-Gauss-Seidel method and Chen's method in 2001.

关 键 词：大型稀疏非线性方程组 不精确牛顿法 经典牛顿法 并行算法 稀疏矩阵 电力系统 潮流方程 

分 类 号：O175.14[理学—数学] O242.23[理学—基础数学]